Basic Math question and answers for November 05, 2024
- Q If 1,200 cm of material is available to make a box with a square base and an open top, find the largest possible volume of the box.cm
- Q A rectangular piece of land is to be fenced using two kinds of fencing. Twoopposite sides will be fenced using standard fencing that costs $6/m, whilethe other two sides will...
- Q (a) Find an equation of the tangent plane to the surface at the given point.x2 + y2 + z = 19, (1, 3, 3)
- Q Find the point(s) on the surface at which the tangent plane is horizontal.z = 9-x - y + 4y(x, y, z) = ()
- Q A sociologist determines that a foreign-language student has learned N(t) = 20t - 2 vocabulary terms after t hours of uninterrupted study.a. How many terms are learned between times t...
- Q Consider h(x) = 5x +7-x +7xDetermine the intervals on which h is concave down.h is concave down on:h is concave down nowhere.Determine the intervals on which his concave up.h is...
- Q Find the directional derivative of the function at P in the direction of v. f(x, y) = x-y, P(6, 5), v =?2/2(i+j)
- Q Archaeologists used pieces of burned wood, or charcoal, found at the site to date prehistoric paintings and drawings on walls and ceilings of a cave in Lascaux, France. Use the...
- Q Which of the following functions of x is guaranteed by the Extreme Value Theorem to have an absolute maximum on the interval [0, 4]? y = sinxy = sin-xy=tanxy =x-16/x+x-20
- Q Find an equation for the tangent line to the graph of y = (x - 9x) ^10 at the point ( 3,0).The equation of the tangent line is y=.(Simplify your...
- Q A thermometer is removed from a room where the temperature is 70 F and is taken outside, where the air temperature is 30 F. After one-half minute the thermometer reads...
- Q The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at time t and has a half-life of 3.3 hours. If 1 gram of this...
- Q A pizza pan is removed at 8:00 PM from an oven whose temperature is fixed at 400F into a room that is a constant 73F. After 5 minutes, the pizza...
- Q Let f(x) = (6 + 3x)f(x) has one critical value at A =For x < A, f(x) isFor x> A, f(x) is
- Q The marginal cost of a product can be thought of as the cost of producing one additional unit of output. For example, if the marginal cost of producing the 50th...
- Q The depth of a rain puddle D(t) is given in inches, and t is given in minutes. If the depth is changing with respect to time, which expression gives the...
- Q Consider the surface z=f(x,y) = 3x + 5y +1 and the curve C in the xy-plane given parametrically as x= cost and y=sint where Osts2.a. Find z'(t).b. Imagine that you...
- Q The profit from the expenditure of x thousand dollars on advertising is given by P(x) = 1,130+35x-2x. Find the marginal profit when the expenditure is x = 15.A. -25 thousand...
- Q 3. A dairy farmer plans to fence in a rectangularpasture adjacent to a river. The river serves as oneborder to the pasture, so the farmer does not need afence along...
- Q Kim was at the top of a 15 foot ladder when the ladder began to slide down the wall. The angle that the base of the ladder makes with the...
- Q A manufacturer of handcrafted wine racks has determined that the cost to produce x units per month is given by C = 0.4x +9,000. How fast is the cost per...
- Q Your company wants to make the largest and most luxurious rectangular dog kennels possible with 72 feet of fencing. The design of the kennel is to use the back side...
- Q Consider the function on the interval (0, 2?).f(x) = ?3 sin x + cosx(a) Find the open intervals on which the function is increasing or decreasing. (Enter your answers using...
- Q Find a, b, c, and d such that the cubic function f(x) = ax + bx + cx + d satisfies the given conditions.Relative maximum: (3, 15)Relative minimum: (5, 13)Inflection...
- Q (5) A straight piece of wire of 28 cm is cut into two pieces. One piece is bent into a square (ie., dimensions x times x.) The other piece is...
- Q Suppose the velocity v of a motorboat coasting in water satisfies the differential equation dv/dt=kv. The initial speed of the motorboat is v(0) = 1 m/s. The speed at 2...
- Q Find all the zeros of f(x) = x^3 + 2x^2 - 5x - 6 given that x = -3 is one of its zeros.
- Q The length of a rectangle is increasing at a constant rate of 3 cm/s, and its width is increasing at a constant rate of 0.5 cm/s. At the time the...
- Q A manufacturing plant calculates its Cost function, C(x), to be C(x) = x - 4x + 50/x and its Revenuefunction, R(x), to be R(x) = 50x. Construct the Profit function,...
- Q Your new house sits at a perpendicular distance of 6 miles from the county highway across a flatparcel of land. The town where you work is 15 miles down the...
- Q Two rows of three cattle pens are going to be built using 400 meters of fencing. Each pen will be rectangular, the same size and the pens will form a...
- Q A company manufactures and sells x television sets per month. The monthly cost and price-demand equations are C(x) = 73,000 + 70x and p(x) = 250--(A) Find the maximum revenue.(B)...
- Q In 1958, you could buy an Edsel Citation convertible for $3800. Cars often depreciate in value rapidly, but one of these convertibles in "winning-show" condition could sell for up to...
- Q Since 1915, the infant mortality rate (in number of deaths per 1000 live births) could be approximated by the equation r(t) = 0.01t - 2t + 97, where t is...
- Q You regularly pay your nephew to drive a semi hauling hay a distance of 170 miles. You have just learned that the stretch of highway that he drives no longer...
- Q 11A 5-foot ladder is leaning against a vertical wall. If the bottom of the ladder is being pulled away from the wall at the rate of 2 feet per second,at...
- Q The radius of the base of a cylinder is increasing at a rate of 7 millimeters per hour.The height of the cylinder is fixed at 1.5 millimeters.At a certain instant,...
- Q 9. Suppose that a product has a revenue function given by R(x) = 2500x - 2x and a cost function given by C(x) = x + 2x + 1000. Find...
- Q A ball is thrown vertically upward. After f seconds, its height / (in feet) is given by the function h(t)-1161-167. What is the maximum height that the ballwill reach?
- Q A rectangle has a length of 11 inches and a width of 2 inches whose sides are changing. The length is increasing by 5 in/sec and the width is growing...
- Q A ball is thrown vertically upward from the ground with an initial velocity of 105 ft/sec. Use h = -16t + vot + ho.Step 2 of 2: Determine what the...
- Q Find the absolute maximum and minimum, if either exists, for the function on the indicated interval.f(x) = 2x-36x +210x+4(A) [-2, 10] (B) [-2,7] (C) [6, 10](A) Find the absolute maximum....
- Q Susan throws a softball upward into the air at a speed of 32 feet per second from a 40-foot platform. The height of the ball after seconds is given by...
- Q The marketing research department of a computer company used a large city to test market the firm's new laptop. The department found the relationship between price p (dollars per unit)...
- Q Find dy/dx and dy/dx2, and find the slope and concavity (if possible) at the given value of the parameter. (If an answer does not exist, enter DNE.)Parametric Equations Pointx =...
- Q A rectangular plot of farmland will be bounded on one side by a river and on the other three sides by a single-strand electric fence. With 500 m of wire...
- Q A company sells widgets. The amount of profit, y, made by the company, is related tothe selling price of each widget, x, by the given equation. Using this equation, find...
- Q The percent of concentration of a certain drug in the bloodstream x hr after the drugis administered is given by K(x) = How long after the drug has been 3x...
- Q Find all the points on the following curve that have the given slope.x=8 cost, y = 8 sint; slope =1/2Select the correct answer below and, if necessary, fill in the...
- Q The function f(x) =2x + 30x - 144x +9 has one local minimum and one local maximum.This function has a local minimum at x =with valueand a local maximum at...
- Q The amount of carbon-15 in a given sample decays exponentially with time. If the function C(m)=100(1/2)^24m models the amount of carbon remaining in the sample after m minutes, which the...
- Q Find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.)/ 7x5 +6/x + 6x dx
- Q If-3x + xy -4 = 0 then find d^2y / dx^2 at the point (-2,1) in simplest form.
- Q A stone is thrown vertically upward from a platform that is 16 feet above ground at a rate of 50 feet per second. Use the projectile formula h = -...
- Q A spherical weather balloon is being inflated. The radius of the balloon is increasing at the rate of 5 cm/s. Express the surface area of the balloon as a function...
- Q A company runs food service concessions for sporting events throughout the country. Their marketing research department chose a particular football stadium to test market a new jumbo hot dog. It...
- Q A fence must be built to enclose a rectangular area of 5000 ft2. Fencing material costs $2 per foot for the two sides facing north and south and $4 per...
- Q For the given cost functionC(x) = 25600 + 800x + x find :a) The production level that will minimize the average cost b) The minimal average cost
- Q A ball is thrown into the airfrom the roof of a 200 foot tall building with an initial upward velovity of 80 ft/sec. Its height function is given by h(t)...
- Q Katie want to build a rectangular enclosure for your pet rabbit, Sniper, against the side of her house. She has bought 150 feet of fencing. What are the dimensions of...
- Q Water flows into a hemispherical tank of radius 10feet (flat side up). At any instant, let h denote thedepth of the water, measured from the bottom, rthe radius of the...
- Q Find f givent that f'(x) = 4x - 5 and f(2) = 5.a) f(x) = 4x + 2b) f(x) = 2x - 5x + 5c) f(x) = 2x 52+7d) f(x)...
- Q The monthly average high temperatures in degrees Fahrenheit at a beach can be modeled by P(x) = 0.0143x4 -0.425x3 +3.545x2-6.256x+64, where x = 1 corresponds to January and x =...
- Q For a certain automobile, M(x) = - .015x +1.22x-7.8, 30 ?x? 60, represents the miles per gallon obtained at a speed of x miles per hour(a) Find the absolute maximum...
- Q Let g(x) = - 3x + 9x + 4x + 5:a) g'(x) =b) g''(x) =c) For which value(s) of a does f''(x) = 0? (Enter you answers as a comma...
- Q A county realty group estimates that the number of housing starts per year over the next three years will be H(r) = 200/ (1+0.03r) where r is the mortgage rate...
- Q Consider the following parametric equations.a. Eliminate the parameter to obtain an equation in x and y.b. Describe the curve and indicate the positive orientation.x=r-4, y=r-1, -3?r?3a. Eliminate the parameter to...
- Q Use the derivative f'(x)= (x-3)(x + 1)(x + 4) to determine the local maxima and minima of f and the intervals of increase and decrease. Sketch a possible graph of...
- Q A farmer decides to enclose a rectangular garden, using the side of a barn as one side of the rectangle. What is the maximum area that the farmer can enclose...
- Q The projected year-end assets in a collection of trust funds, in trillions of dollars, where t represents the number ofyears since 2000, can be approximated by the following function where...
- Q The radius r of a circle is increasing at a rate of 8 centimeters per minute. Find the rate of change of the area whenr = 30 centimeters.cm/min
- Q A winch at the top of a 12-meter building pulls a pipe of the same length to a vertical position, as shown in the figure. The winch pulls in rope...
- Q When a certain polyatomic gas undergoes adiabatic expansion, its pressure p and volume V satisfy the equation pv1.4 = k, where k is a constant. Find the relationship between the...
- Q Determine the location and value of the absolute extreme values of f on the given interval, if they exist.f(x)=30x(1/2)-x on [0,900]What is/are the absolute maximum/maxima of f on the given...
- Q Consider the following scenarios using two strings.Part A: Is it possible to construct a square with the two strings? Explain youranswer.Part B: Is it possible to construct a rectangle with...
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